To make the puff pastry cases, preheat the oven to 180 degrees Celsius (350 Fahrenheit).
Add the egg yolk and milk to a ramekin and mix to get a smooth runny mixture.
Roll out the puff pastries, and use a cookie cutter of 6 cm (2.5 inches) in diameter to cut out a circle.
Cut out another circle, and place a cookie cutter of 4 cm ( 1.5 inches) in diameter in the middle of the circle and press down to cut out a smaller circle.
Repeat with the rest of the puff pastry.
Place all the larger circles onto 2 baking trays lined with non-stick paper and brush with the egg mixture.
Place the dough rings on top of each circle and brush them as well - the small circles are not needed for the vol-au-vents, but can be baked separately as used as lids.
Bake for 20 minutes or until the cases are golden.
To make the filling, peel and chop the onion and garlic.
Add the butter and oil to a frying pan set over a medium heat, and allow the butter to melt.
Add the onion and fry it until golden, then add the garlic and chicken cut into pieces, and cook everything until the chicken is tender - it can take up to 5-6 minutes depending on the size of the chicken pieces.
Add the chopped mushrooms and continue to cook until they release all their liquid.
Sprinkle the flour over the chicken and mushrooms, and pour in the milk, whisking well until the milk thickens into a sauce.
Add the grated parmesan, season with salt and pepper, and garnish with parsley or dill.
Fill each pastry case with the filling and serve hot or cold.